Handbook

The course begins with a revision and extension of material on vector spaces, linear transformations, basis and dimension from first year. It also covers inner products over both the real and complex fields, orthogonalization, reflections, QR factorizations and unitary, self-adjoint and normal transformations. It then turns to the study of eigenvalues and eigenvectors, diagonalization and Jordan forms and functions of matrices. The course also includes applications to linear systems of differential equations, quadratics and rotations as time permits. The course is primarily but not exclusively intended for students aiming to complete honours in applied mathematics, pure mathematics, statistics or data science, and so where content is in common with MATH2501, MATH2601, aims to give students a deeper level of understanding. The course consists of lectures and tutorials, where the latter may be run as active classrooms.